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A two-dimensional fractional thermoviscoelastic problem for solid sphere under axisymmetric temperature distribution is presented. The solution of the problem is obtained in the Laplace transform domain by using a direct approach. The surface of the sphere is taken to be traction-free and subjected to the given axisymmetric temperature distribution. The inversion of the Laplace transform is carried out using the inversion formulas of the transform together with Fourier expansion techniques. Numerical results are represented graphically and discussed.

Effect of Atangana–Baleanu fractional derivative on a two-dimensional thermoviscoelastic problem for solid sphere under axisymmetric distribution